Semi-empirical Haken–Strobl model for molecular spin qubits

Abstract

Understanding the physical processes that determine the relaxation T _1 and dephasing T _2 times of molecular spin qubits is critical for envisioned applications in quantum metrology and information processing. Recent spin-echo measurements of solid-state molecular spin qubits have stimulated the development of quantum mechanical models for predicting intrinsic qubit timescales using first-principles electronic structure methods. We develop an alternative semi-empirical approach to construct Redfield quantum master equations for molecular spin qubits using a stochastic Haken–Strobl theory for a central spin with fluctuating gyromagnetic tensor due to spin-lattice interaction and fluctuating local magnetic field due to interactions with lattice spins. Using two vanadium-based spin qubits as case studies, we compute qubit population and decoherence times as a function of temperature and magnetic field, using a bath spectral density parametrized with a small number of T _1 measurements. The theory quantitatively agrees with experimental data over a range of conditions beyond those used to parameterize the model, demonstrating the generalization potential of the method. The ability of the model to describe the temperature dependence of the ratio $T_2/T_1$ is discussed and possible applications for designing novel molecule-based quantum magnetometers are suggested.

Keywords

• molecular spin qubits
• Redfield equation
• Haken–Strobl theory
• spin-lattice interaction
• spectral density
• electron spin resonance